Optimal response of half car vehicle model with sky-hook damper using LQR with look ahead preview control

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Optimal response of half car vehicle model with sky‑hook damper using LQR with look ahead preview control L. V. V. Gopala Rao1 · S. Narayanan2 Received: 23 July 2019 / Accepted: 4 August 2020 / Published online: 14 August 2020 © The Brazilian Society of Mechanical Sciences and Engineering 2020

Abstract This paper addresses the problem of determining the optimal parameters of a sky-hook damper type suspension in the control of the stationary random response of half car vehicle models traversing a rough road with constant velocity. The feedback control scheme is realized by approximating the sky-hook damper strategy, and the optimal parameters of the sky-hook damper are obtained by equating the sky-hook damper suspension force with that of a fully active suspension force using linear quadratic regulator with preview control (LQR with preview control). Results show that the overall performance of the sky-hook damper approximately 99% matches with performance of LQR with preview control (look ahead preview control) over a specified vehicle velocity range. Keywords  Half Car · Sky-hook damper · Preview control · Optimization · Semi-active suspension

1 Introduction The active suspension system improves the performance of vehicle by counteracting the road excitations through an actuator. Some of the drawbacks of the active suspension systems are the time lag, less robustness and more cost restrict the use of active suspension. To overcome some of these draw backs of active suspension, semi-active suspensions are introduced. In this context, the idea of sky-hook type semi-active suspensions has been introduced for vehicle suspensions by Crosby and Karnopp [1]. Karnopp et al. [2] have tried to realize the sky-hook concept in a moving vehicle as a variable rate damper. Liu et al. [3] used five controls to study the semi-active damper performance using on–off sky-hook, adaptive damping, continuous sky-hook and continuous control. Sammier et al. [4] proposed a continuous feedback control strategy to approximately realize the sky-hook damper Technical Editor: Wallace Moreira Bessa, D.Sc. * L. V. V. Gopala Rao [email protected] 1



Department of Mechanical Engineering, Vignan’s Institute of Information Technology, Duvvada, Visakhapatnam 530 049, India



Department of Mechanical Engineering, Indian Institute of Information Technology, Design and Manufacturing, Kancheepuram, Chennai 600 127, India

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control. Valasek et al. [5] introduced extended ground-hook control strategy concept for off-road vehicle suspensions. Li and Nagai [6] used sky-hook control to increase the ride comfort of railway vehicle models. Vladimir and Marian [7] used genetic algorithm optimization method to optimize half car vehicle model parameters like damping coefficients and stiffness coefficients. Rao and Narayanan [8] used new methodology to optimize the skyhook damper parameters of half car vehicle model by equating the active suspension control force using linear quadratic regulator (LQR) with that of the sky-hook damper suspen